On The Breakdown Properties of some Multivariate M-Functionals

For probability distributions on ℝq, a detailed study of the breakdown properties of some multivariate M-functionals related to Tyler's [Ann. Statist. 15 (1987) 234] ‘distribution-free’ M-functional of scatter is given. These include a symmetrized version of Tyler's M-functional of scatter, and the multivariate t M-functionals of location and scatter. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M-functional of scatter and of its symmetrized version are 1/q and inline image, respectively. For the multivariate t M-functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/(q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low-dimensional subspaces.

Strengthening the food systems governance evidence base: Supporting commensurability of research through a systematic review of methods

Governance of food systems is a poorly understood determinant of food security. Much scholarship on food systems governance is non-empirical, while existing research is often case study-based and theoretically and methodologically incommensurable. This frustrates aggregation of evidence and generalisation. We undertook a systematic review of methods used in food systems governance research with a view to identifying a core set of indicators for future research. We gathered literature through a structured consultation and sampling from recent reviews. Indicators were identified and classified according to the levels and sectors they investigate. We found a concentration of indicators in food production at local to national levels and a sparseness in distribution and consumption. Unsurprisingly, many indicators of institutional structure were found, while agency-related indicators are moderately represented. We call for piloting and validation of these indicators and for methodological development to fill gaps identified. These efforts are expected to support a more consolidated future evidence base and eventual meta-analysis.